A 0.001 molal aqueous solution of a complex `[MA_8]` has the freezing point of `-0.0054^(@)C`. If the primary valency of the salt undergoes 100% ionization and `K_f` for water =1.8 K molality^(-1) the correct representation of complex is

Options

A. `[MA_8]`
B. `[MA_6]A_2`
C. `[MA_4]A_4`
D. `[MA_5]A_3`

Answer

To solve the problem, we need to determine the correct representation of the complex `[MA_8]` based on the given data. Here's a step-by-step solution:

### Step 1: Understand the given data
- We have a 0.001 molal aqueous solution of the complex `[MA_8]`.
- The freezing point depression (ΔTf) is given as -0.0054°C.
- The cryoscopic constant (Kf) for water is 1.8 K kg mol⁻¹.
- The primary valency of the salt undergoes 100% ionization.

### Step 2: Calculate the freezing point depression
The formula for freezing point depression is:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where:
- ΔTf = freezing point depression
- i = van 't Hoff factor (number of particles the solute breaks into)
- Kf = cryoscopic constant
- m = molality of the solution

### Step 3: Rearranging the formula to find i
We can rearrange the formula to solve for the van 't Hoff factor (i):
\[ i = \frac{\Delta T_f}{K_f \cdot m} \]

### Step 4: Substitute the values into the equation
Substituting the known values into the equation:
\[ i = \frac{0.0054}{1.8 \cdot 0.001} \]

### Step 5: Calculate i
Now, calculate the value of i:
\[ i = \frac{0.0054}{0.0018} = 3 \]

### Step 6: Interpret the value of i
The van 't Hoff factor (i) indicates that the complex dissociates into 3 particles in solution. This means that the complex can be represented as:
- M + 2A (for example, M could be a cation and A could be an anion).

### Step 7: Determine the correct representation of the complex
Since we have 3 ions from the complex, we can represent the complex as:
\[ [MA_6A^{2+}] \]
This means that one metal ion (M) is combined with six anions (A) and two of them are contributing to the charge balance.

### Conclusion
The correct representation of the complex is:
\[ [MA_6A^{2+}] \]